In order to determine pavement condition for airport runways or highways, the load bearing capability of the pavement is periodically tested. Load bearing capability may deteriorate, over time, due to a number of factors, including changes in the elastic moduli of subpavement layers of earth. Thus, when subpavement earth layers subside or swell, their moduli are altered and affect the stability and load bearing capability of an overlying pavement. In order to measure the load bearing capability of the pavement, it is desirable to utilize technologies that are nondestructive so that the integrity of the pavement layer is maintained. Further, the measurements should desirably be made rapidly, through an automated system, to minimize time and reduce costs.
A rolling weight deflectometer may be used to continuously measure the deflection of a pavement. A device of this type is disclosed in U.S. Pat. No. 4,571,695 (“the '695 patent”). In essence, a load is placed on a wheel that rolls across the pavement and the depth of a deflection basin created by the loaded wheel is measured using precision laser sensors mounted on a horizontal member that tracks with the wheel. Such deflection measurements provide insight into the load bearing capability of the pavement. However, pavement deflections are usually very small, typically 0.010 to 0.040 inch for a 20,000 pound applied load. Therefore, not only are extremely sensitive sensors required to measure the deflection, but the sensors should have a stable reference plane. The deflectometer of the '695 patent fails to meet both of these requirements, as will be explained below.
FIG. 3 is a schematic representation of a rolling weight deflectometer, showing a member 20, a load wheel 22, and the pavement sensors 52, 54, 56, and 58. The upper schematic of FIG. 3 shows the horizontal bearing member at a first position on the pavement at time t1, while the lower schematic shows the member at a second position at time t2. The direction of travel of the member is indicated by an arrow and the amount of travel is metered by a “fifth wheel” (not shown). The reading or sampling control system of the apparatus is dependent upon the amount of rotation of the fifth wheel or odometer which sends electrical pulses to a computer to trigger the taking of measurements by the sensors. Thus, the pavement sensors are activated to take measurements at a spacing equal to the sensor separation distance. Sensor 52 measures that part of the depression basin formed that extends vertically below the sensor at P1. This is not the exact maximum point of deflection, which should be directly beneath the center of load wheel 22. However, since the sensor is mounted as close as possible to a side of the wheel (typically, about 5 to 9 inches from the center of the wheel), the error introduced is acceptable. Likewise, equidistantly spaced sensors 54, 56, and 58 measure distances to points P2, P3, and P4, respectively. After the trailer has moved forward by one sensor separation distance, the sampling control system is again activated by the rotation of the odometer wheel. Load wheel 22 has now moved so that a line drawn vertically through the axis of the sensor 52 passes through the point P2 (in a statistical sense), where sensor 54 was previously positioned. Likewise, sensors 54, 56, and 58 have moved horizontally in the same direction for the same distance, so that sensor 54 is directly above P3, sensor 56 is directly above P4, and sensor 58 is directly above a new point, P5. Thus, it is clear that a reading will be taken at each Pn, by the deflection basin measuring sensor 52, and each of the other sensors 54, 56, and 58, in a statistical sense. This assumes that the odometer wheel is accurate and precise, and that the trailer is traveling in a straight line.
FIG. 4 is a schematic showing the determination of the height of a point Pi on pavement P above or below a horizontal theoretical datum line L. As shown, distance sensors 54, 56, and 58 are equally spaced. Sensor 54 is a distance C from a point Pc vertically beneath the sensor on the pavement. Likewise, sensors 56 and 58 are distances B and A, respectively, from points Pb and Pa on the pavement. As for the description of FIG. 3, when the beam 20 is moved in the direction of travel indicated by the arrow, the odometer wheel (not shown) rotates and a second reading is taken such that sensor 52 (not shown), equally spaced from and left of sensor 54 and located nearest the load wheel, is a distance C′ directly above Pc. Likewise, sensor 54 is above point Pb, sensor 56 is above point Pa, and sensor 58 has moved a distance to be above a new point (not shown). Thus, sensor 52 detects deflection of the pavement at statistically the same location where the unloaded pavement was measured by sensor 54. By continuing the pavement traversal process, sensor 52 measures statistically the same pavement, under load conditions, as measured by sensors 54, 56 and 58 under no load conditions.
The geometry of undeflected pavement is determined using leading sensors 54, 56, and 58, which are, in this example, equally spaced apart. Referring to FIG. 4, the point of contact Pb of a laser beam from central sensor 56 with the pavement is at a measured distance B. A line is projected from Pa, a point of contact of a laser beam from sensor 58 through Pb, to intersect a laser beam extending vertically from sensor 54 to the pavement at point Pi. The distance that Pa is below the datum line L, is given by (A-B). Similarly, from geometry, this distance (A-B) between point Pi and the datum line L is reproduced. However, this does not account for the distance between the datum line L and Pc. Thus, h is defined as the distance between Pc and Pi and is called a “virtual height.” Since sensors 54 and 58 are at equal elevation above datum line L, the following equality holds:A−(A−B)=C−h+(A−B)  (I)This equation simplifies to:h=A−2B+C  (II)
In order to determine pavement deflection, the geometry of a second measurement, subject to the load wheel, is determined using sensors 52, 54, and 56. In this instance, the distance between sensors 52 and 54 may not be equal to the distance between sensors 54 and 56 and 56 to 58. The use of unequal distances between sensors allows the construction of a more compact rolling weight deflectometer. The following derivation of pavement deflection δ is based on a rolling weight deflectometer where the distances between sensors 52 and 54, 54 and 56 are each different. But, the distance between sensors 54 and 56, and sensors 56 and 58 are equal. To calculate the virtual height h′, the same analysis as above is applied. Measured distances B, C, and D extend from sensors 56, 54, and 52, respectively, to the pavement surface directly beneath the sensors. The beams from sensors 56, 54, and 52, contact the pavement P at points Pb, Pc, and Pd, respectively. A theoretical straight line is projected from Pb through Pc to intersect the vertical laser beam emitted from sensor 52 (the sensor axis of sensor 52) at point Pn. The distance from Pb to the theoretical horizontal datum line L is (B−C). By the geometry of similar triangles, the distance between the datum line L and Pn is (n/m)(B−C). We can equate the elevation of the sensors:B−(B−C)=D−h′+((n/m)(B−C))  (III)or, simplifyingh′=(n/m)B−(1+(n/m))C+D  (IV)
where (n/m) is always greater than or equal to 1, and depends upon the relative spacing between the sensors.
Pavement deflection δ is then determined as:h−h′=δ  (V)
Aside from the factors discussed above, errors may be introduced into the h and h′ calculations by thermal deformation of member 20. A member 20 of thickness H, thermal coefficient of expansion γ, and subject to temperature differential ΔT across its thickness, will be bent into a radius of curvature R, where: #
  R  =      H          γΔ      ⁢                          ⁢      T      
The deflection, d, at the center of the member of length L, will be:
  d  =      R    -                            R          2                -                              L            2                    4                    
If R is very much larger than L, then this simplifies to:
  d  =                    L        2            ⁢      γΔ      ⁢                          ⁢      T              8      ⁢      H      
For a member that is a steel beam 30 feet long with γ=11×10−6 per ° C., and H=10 inches, the thermal deflection is 0.018 inches/° C.
Since the deflections are typically in the range 0.015 to 0.040 inch for 20,000 pound loads, the thermally induced effect is about 50% of the maximum expected deflection.
Vibrational bending has similar deleterious effects on accuracy of deflection measurements. Vibration can be viewed as a dynamic type of member bending where member displacement varies with time. The actual effects are complex to model, but it is expected that the distance sensors would not each be displaced by the same distance from their horizontal alignment with each other.
Despite the sophistication and ease of use of the rolling weight deflectometer, the apparatus has inherent flaws that lead to significant errors in pavement deflection measurements. Measurements are based on several assumptions, including that the horizontal member remains absolutely straight and steady at all times. However, the horizontal member may bend due to thermal effects, despite sunshading, and may vibrate as the member is transported. Member bending introduces significant errors since pavement deflection is usually quite small, member bending effects are often large relative to actual pavement deflection. Also, it is assumed that the deflectometer tracks in a sufficiently straight line so that successive pavement distance sensors “see” the same spots on the pavement in deflected and undeflected condition. In practice, this assumption may not hold.
In addition, the following factors contribute to additional errors in pavement deflection measurements:                1) As the vehicle travels around curves in the road, the vehicle follows the trajectory of the road, while the height sensors, which are connected by a straight reference beam, follow different paths.        2) Measured deflections are small in comparison to pavement surface topology variation so that the spatially averaged height measured at one location might vary significantly if the average height is measured at a slightly offset location. Accordingly, the 3 sequential measurements of a given pavement location must be as close to the same position as possible.        3) Even on straight roads, it is difficult for the vehicle operator to maintain a straight line trajectory. Although increased vehicle speeds can mitigate this problem to a certain extent, vehicle wander is still a problem.        4) Road crown and road slope can cause the vehicle to “crab,” wherein the path of the rear wheels of the trailer are offset laterally, i.e., to the left or right from the path of the front wheels. As a result, the 4 sensors on the reference beam view parallel lines of pavement as the vehicle moves forward.        5) Variations in road topology cause the vehicle and, therefore, the reference beam to roll, sway, and pitch.        
There exists a need for a rolling weight deflectometer that compensates for variation in the location of the measured spot from one laser sensor to the next in order to provide more accurate measurements of pavement deflection under load. Further, the deflectometer should have all of the advantages of present rolling weight deflectometers, namely, ease of use, mobility, high sampling rate, and continuous operation to reduce the time and cost of taking measurements, as well as operator exposure to traffic. The deflectometer should also have built-in compensation for out-of-perfect straight line tracking of the trailer.